Iterated Bootstrap
- Repeatedly resample the original dataset with replacement to create many new datasets and compute the statistic on each.
- Use the collection of estimates to approximate the statistic’s sampling distribution (e.g., mean or standard error).
- Especially helpful when the original dataset is small or the sampling distribution is not well known.
Definition
Section titled “Definition”The iterated bootstrap is a statistical method that involves resampling a dataset with replacement to generate multiple new datasets, each used to estimate the sampling distribution of a statistic. This process is repeated multiple times to create a large number of estimates, which are then used to provide a more accurate representation of the true sampling distribution of the statistic.
Explanation
Section titled “Explanation”Starting from the original dataset, the iterated bootstrap repeatedly draws samples with replacement to form many “bootstrap” datasets. For each bootstrap dataset, the statistic of interest is computed. Collecting these repeated estimates produces an empirical approximation of the statistic’s sampling distribution. The resulting distribution can be used to assess properties of the estimator (such as variability) and to form more robust estimates when the theoretical sampling distribution is unknown or the original sample is small.
Examples
Section titled “Examples”Estimating a mean
Section titled “Estimating a mean”Suppose we have a dataset of 100 observations and we want to estimate the mean. Use the iterated bootstrap to generate multiple new datasets by resampling the original dataset with replacement. For each new dataset, calculate the mean and record the result. By repeating this process a large number of times, create a large number of mean estimates, which can be used to construct a more accurate representation of the true sampling distribution of the mean.
Estimating a standard error
Section titled “Estimating a standard error”Suppose we have a dataset of 100 observations and we want to estimate the standard error of the mean. Use the iterated bootstrap to generate multiple new datasets by resampling the original dataset with replacement. For each new dataset, calculate the mean and the standard error of the mean. By repeating this process a large number of times, create a large number of standard error estimates, which can be used to construct a more accurate representation of the true sampling distribution of the standard error.
Use cases
Section titled “Use cases”- Improving the accuracy of statistical estimates when the original dataset is small.
- Estimating properties of an estimator (such as variability) when the sampling distribution of the statistic is not well known.
Related terms
Section titled “Related terms”- Bootstrap
- Resampling
- Sampling distribution
- Standard error